91影视

The Integral is given as,

${鈭�}_{x_0}^{\mathrm{鈭�}}{x}^{b}dx$.

Integration concept used

In order to calculate the conditions under which the given integral may diverge, start by writing the integral as follows:

${鈭�}_{x_0}^{\mathrm{鈭�}}{x}^{b}dx$

Here, $\text{dx}$ is called the differential of the variable$x$.

The upper limit of the Integral is 8.

Integrating the above-given function under the given limits we will get

${鈭�}_{x_0}^{\mathrm{鈭�}}{x}^{b}dx={\left[\frac{x^{b+1}}{b+1}\right]}_{x_0}^{\mathrm{鈭�}}$

The function will keep on diverging unless $b$ is less than $-1$ hence we can say the integral will diverge at the given infinite limit (upper limit). The value of b equal to $-1$ cannot be possible because it would make the entire function infinite.

Now, for the total integral to not diverge, it is necessary for the ${蠄}^2$ to fall off more rapidly or at least as rapid as $|x{|}^{鈭�1}$ and $蠄$to fall off more rapidly or at least as rapid as$|\text{x}{|}^{鈭�1/2}$ .